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1936:; Armitage-Caplan, C.; Arnaud, M.; Ashdown, M.; Atrio-Barandela, F.; Aumont, J.; Baccigalupi, C.; Banday, A. J.; Barreiro, R. B.; Bartlett, J. G.; Battaner, E.; Benabed, K.; BenoĂźt, A.; Benoit-LĂ©vy, A.; Bernard, J.-P.; Bersanelli, M.; Bielewicz, P.; Bobin, J.; Bock, J. J.; Bonaldi, A.; Bond, J. R.; Borrill, J.; Bouchet, F. R.; Bridges, M.; Bucher, M.; Burigana, C.; Butler, R. C.; Calabrese, E.; et al. (2014). "Planck2013 results. XVI. Cosmological parameters".
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2530:; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A. J.; Barreiro, R. B.; Bartlett, J. G.; Bartolo, N.; Battaner, E.; Battye, R.; Benabed, K.; Benoit, A.; Benoit-Levy, A.; Bernard, J. P.; Bersanelli, M.; Bielewicz, P.; Bonaldi, A.; Bonavera, L.; Bond, J. R.; Borrill, J.; Bouchet, F. R.; Boulanger, F.; Bucher, M.; Burigana, C.; Butler, R. C.; Calabrese, E.; et al. (2020). "Planck 2018 results. VI. Cosmological parameters".
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1240:. For instance, one can imagine finding a gas cloud that is not in thermal equilibrium due to being so large that light speed cannot propagate the thermal information. Knowing this propagation speed, we then know the size of the gas cloud as well as the distance to the gas cloud, we then have two sides of a triangle and can then determine the angles. Using a method similar to this, the
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1466:, i.e., possess positive curvature, the topology is compact. For a flat (zero curvature) or a hyperbolic (negative curvature) spatial geometry, the topology can be either compact or infinite. Many textbooks erroneously state that a flat or hyperbolic universe implies an infinite universe; however, the correct statement is that a flat universe that is also
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the universe's global geometry can be constructed, all consistent with current observations and general relativity. Hence, it is unclear whether the observable universe matches the entire universe or is significantly smaller, though it is generally accepted that the universe is larger than the observable universe.
825:. The global topology of the universe cannot be deduced from measurements of curvature inferred from observations within the family of homogeneous general relativistic models alone, due to the existence of locally indistinguishable spaces with varying global topological characteristics. For example; a
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are ignored, then the curvature of the universe can be determined by measuring the average density of matter within it, assuming that all matter is evenly distributed (rather than the distortions caused by 'dense' objects such as galaxies). This assumption is justified by the observations that, while
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If the observable universe encompasses the entire universe, we might determine its structure through observation. However, if the observable universe is smaller, we can only grasp a portion of it, making it impossible to deduce the global geometry through observation. Different mathematical models of
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is longer in one dimension than the others. Scientists test these models by looking for novel implications â phenomena not yet observed but necessary if the model is accurate. For instance, a small closed universe would produce multiple images of the same object in the sky, though not necessarily of
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One of the unanswered questions about the universe is whether it is infinite or finite in extent. For intuition, it can be understood that a finite universe has a finite volume that, for example, could be in theory filled with a finite amount of material, while an infinite universe is unbounded and
1290:, that is, modeling the matter within the universe as a perfect fluid. Although stars and structures of mass can be introduced into an "almost FLRW" model, a strictly FLRW model is used to approximate the local geometry of the observable universe. Another way of saying this is that, if all forms of
1018:. An example of a positively curved space would be the surface of a sphere such as the Earth. A triangle drawn from the equator to a pole will have at least two angles equal 90°, which makes the sum of the 3 angles greater than 180°. An example of a negatively curved surface would be the shape of a
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with an unknown global topology. It is currently unknown whether the universe is simply connected like euclidean space or multiply connected like a torus. To date, no compelling evidence has been found suggesting the topology of the universe is not simply connected, though it has not been ruled out
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When cosmologists speak of the universe as being "open" or "closed", they most commonly are referring to whether the curvature is negative or positive, respectively. These meanings of open and closed are different from the mathematical meaning of open and closed used for sets in topological spaces
1989:
De
Bernardis, P.; Ade, P. A. R.; Bock, J. J.; Bond, J. R.; Borrill, J.; Boscaleri, A.; Coble, K.; Crill, B. P.; De Gasperis, G.; Farese, P. C.; Ferreira, P. G.; Ganga, K.; Giacometti, M.; Hivon, E.; Hristov, V. V.; Iacoangeli, A.; Jaffe, A. H.; Lange, A. E.; Martinis, L.; Masi, S.; Mason, P. V.;
1500:) will not be able to distinguish between a flat, open and closed universe if the true value of cosmological curvature parameter is smaller than 10. If the true value of the cosmological curvature parameter is larger than 10 we will be able to distinguish between these three models even now.
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In the absence of dark energy, a flat universe expands forever but at a continually decelerating rate, with expansion asymptotically approaching zero. With dark energy, the expansion rate of the universe initially slows down, due to the effect of gravity, but eventually increases. The
1411:, have an edge or boundary. Spaces that have an edge are difficult to treat, both conceptually and mathematically. Namely, it is difficult to state what would happen at the edge of such a universe. For this reason, spaces that have an edge are typically excluded from consideration.
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of the whole universeâboth the observable universe and beyond. While the local geometry does not determine the global geometry completely, it does limit the possibilities, particularly a geometry of a constant curvature. The universe is often taken to be a
902:
The observable universe (of a given current observer) is a roughly spherical region extending about 46 billion light-years in all directions (from that observer, the observer being the current Earth, unless specified otherwise). It appears older and more
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These and other astronomical measurements constrain the spatial curvature to be very close to zero, although they do not constrain its sign. This means that although the local geometries of spacetime are generated by the theory of relativity based on
1990:
Mauskopf, P. D.; Melchiorri, A.; Miglio, L.; Montroy, T.; Netterfield, C. B.; Pascale, E.; Piacentini, F.; Pogosyan, D.; et al. (2000). "A flat
Universe from high-resolution maps of the cosmic microwave background radiation".
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A hyperbolic universe, one of a negative spatial curvature, is described by hyperbolic geometry, and can be thought of locally as a three-dimensional analog of an infinitely extended saddle shape. There are a great variety of
1336:; relaxing either of these complicates the analysis considerably. A global geometry is a local geometry plus a topology. It follows that a topology alone does not give a global geometry: for instance, Euclidean 3-space and
2143:; Weeks, Jeff; Riazuelo, Alain; Lehoucq, Roland; Uzan, Jean-Phillipe (2003-10-09). "Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background".
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In the 1990s and early 2000s, empirical methods for determining the global topology using measurements on scales that would show multiple imaging were proposed and applied to cosmological observations.
1733:(i.e., one that is not compact and without boundary). A "closed universe" is necessarily a closed manifold. An "open universe" can be either a closed or open manifold. For example, in the
1075:). The density parameter is the average density of the universe divided by the critical energy density, that is, the mass energy needed for a universe to be flat. Put another way,
2209:
Roukema, Boudewijn; BuliĆski, Zbigniew; Szaniewska, Agnieszka; Gaudin, Nicolas E. (2008). "A test of the
Poincare dodecahedral space topology hypothesis with the WMAP CMB data".
2262:
Boudewijn François
Roukema; Bajtlik S.; Biesiada M.; Szaniewska A.; Jurkiewicz H. (2007). "A weak acceleration effect due to residual gravity in a multiply connected universe".
1734:
1279:
347:
1454:, acceleration effects measured on local scales in the patterns of the movements of galaxies should, in principle, reveal the global topology of the universe.
1708:. For hyperbolic local geometry, many of the possible three-dimensional spaces are informally called "horn topologies", so called because of the shape of the
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1737:(FLRW) model, the universe is considered to be without boundaries, in which case "compact universe" could describe a universe that is a closed manifold.
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relate the local geometry to the global geometry. If the local geometry has constant curvature, the global geometry is very constrained, as described in
1725:
and for the mathematical meaning of open and closed manifolds, which gives rise to ambiguity and confusion. In mathematics, there are definitions for a
1610:. The most familiar such global structure is that of Euclidean space, which is infinite in extent. Flat universes that are finite in extent include the
718:
1430:. The term "without boundary" means that the space has no edges. Moreover, so that calculus can be applied, the universe is typically assumed to be a
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Negative curvature – a drawn triangle's angles add up to less than 180°; such 3-dimensional space is locally modeled by a region of a
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Positive curvature – a drawn triangle's angles add up to more than 180°; such 3-dimensional space is locally modeled by a region of a
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explains that mass and energy bend the curvature of spacetime and is used to determine what curvature the universe has by using a value called the
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the same age. As of 2024, current observational evidence suggests that the observable universe is spatially flat with an unknown global structure.
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1618:. Moreover, in three dimensions, there are 10 finite closed flat 3-manifolds, of which 6 are orientable and 4 are non-orientable. These are the
788:
2404:
Jan J Ostrowski; Boudewijn F Roukema; Zbigniew P BuliĆski (30 July 2012). "A relativistic model of the topological acceleration effect".
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no numerical volume could possibly fill it. Mathematically, the question of whether the universe is infinite or finite is referred to as
1232:
Another way to measure Ω is to do so geometrically by measuring an angle across the observable universe. This can be done by using the
1060:. These depictions of two-dimensional surfaces are merely easily visualizable analogs to the 3-dimensional structure of (local) space.
2333:
Boudewijn François
Roukema; Rozanski P. T. (2009). "The residual gravity acceleration effect in the Poincare dodecahedral space".
3064:
3059:
2918:
49:
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Aurich, Ralf; Lustig, S.; Steiner, F.; Then, H. (2004). "Hyperbolic
Universes with a Horned Topology and the CMB Anisotropy".
2060:
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1607:
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522:
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Janna Levin, Evan
Scannapieco & Joseph Silk (1998). "The topology of the universe: the biggest manifold of them all".
1304:
24:
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is commonly used to model the universe. The FLRW model provides a curvature of the universe based on the mathematics of
1875:
1434:. A mathematical object that possesses all these properties, compact without boundary and differentiable, is termed a
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Assuming a finite universe, the universe can either have an edge or no edge. Many finite mathematical spaces, e.g., a
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in the universe and take its average density, then divide that average by the critical energy density. Data from the
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or mountain pass. A triangle drawn on a saddle surface will have the sum of the angles adding up to less than 180°.
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is a quantity describing how the geometry of a space differs locally from flat space. The curvature of any locally
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implies an infinite universe. For example, Euclidean space is flat, simply connected, and infinite, but there are
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As stated in the introduction, investigations within the study of the global structure of the universe include:
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is called the diameter of the universe, in which case the universe has a well-defined "volume" or "scale".
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1704:, and their classification is not completely understood. Those of finite volume can be understood via the
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and colleagues in 2003 and an optimal orientation on the sky for the model was estimated in 2008.
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whether the geometry of the global universe is flat, positively curved, or negatively curved, and,
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geometry: This relates to the curvature of the universe, primarily concerning what we can observe.
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Scientific
American Blog explanation of a flat universe and the curved spacetime in the universe.
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is the same as that of an open universe in the sense that space will continue expanding forever.
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In the 2000s and 2010s, it was shown that, since the universe is inhomogeneous as shown in the
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has determined that the sum of the angles to 180° within experimental error, corresponding to
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The curvature of the universe places constraints on the topology. If the spatial geometry is
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give values for the three constituents of all the massâenergy in the universe â normal mass (
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2009:
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Crane, Leah (29 June 2024). de Lange, Catherine (ed.). "How big is the universe, really?".
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is a positively curved space, colloquially described as "soccerball-shaped", as it is the
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refers to both its local and global geometry. Local geometry is defined primarily by its
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Zero curvature (flat) – a drawn triangle's angles add up to 180° and the
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2469:"How flat can you get? A model comparison perspective on the curvature of the Universe"
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1999:
1971:
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without boundary. The term compact means that it is finite in extent ("bounded") and
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The latest research shows that even the most powerful future experiments (like the
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The universe may be compact in some dimensions and not in others, similar to how a
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for example) imply that the observable universe is spatially flat to within a 0.4%
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1967:
1829: â Hypothesis that the total amount of energy in the universe is exactly zero
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apart. A finite universe is a bounded metric space, where there is some distance
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the deeper we look into space. In theory, we could look all the way back to the
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to generalize the (intrinsic) notion of curvature to higher-dimensional spaces
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1806: â Differential geometry theoremâThe "remarkable theorem" discovered by
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Fagundes, Helio V. (2002). "Exploring the global topology of the universe".
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1422:, that have no edges. Mathematically, these spaces are referred to as being
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mission, released in 2018, show the cosmological curvature parameter,
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holds; such 3-dimensional space is locally modeled by
Euclidean space
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geometry: This pertains to the universe's overall shape and structure.
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has everywhere zero curvature but is finite in extent, whereas a flat
2021:
1756: â Cosmological modelâA string-theory-related model depicting a
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105:. Statements consisting only of original research should be removed.
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explains how spatial curvature (local geometry) is constrained by
19:"Edge of the universe" redirects here. For the Bee Gees song, see
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is greater than, less than, or equal to 1. From top to bottom: a
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The local geometry of the universe is determined by whether the
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1931:
1800: â List of statements that appear to contradict themselves
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1019:
942:
1712:, a canonical model of hyperbolic geometry. An example is the
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whether the topology is simply connected (for example, like a
1761:
1611:
1535:, consistent with a flat universe. (i.e. positive curvature:
1362:
1105:
to determine the curvature two ways. One is to count all the
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that are flat, multiply connected, finite, and compact (see
222:
2739:
LachiĂšze-Rey, M., Luminet, J.P. (1995). "Cosmic
Topology".
2584:"A Universe From Nothing lecture by Lawrence Krauss at AAI"
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The actual value for critical density value is measured as
845:
2980:
885:
The universe's structure can be examined from two angles:
2467:
Vardanyan, Mihran; Trotta, Roberto; Silk, Joseph (2009).
1606:
In a universe with zero curvature, the local geometry is
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1340:
have the same topology but different global geometries.
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Possible wrap-around dodecahedral shape of the universe
2685:
1988:
1822:
Pages displaying short descriptions of redirect targets
1776:
Pages displaying short descriptions of redirect targets
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Universe is Finite, "Soccer Ball"-Shaped, Study Hints.
1687:, the symmetry of a soccer ball. This was proposed by
1438:. The 3-sphere and 3-torus are both closed manifolds.
2957:
1414:
However, there exist many finite spaces, such as the
1311:
when analyzed at a sufficiently large spatial scale.
813:, while the global geometry is characterised by its
2466:
2080:
1694:
1644:
1383:, there are points that are of a distance at least
868:
148:
may be too technical for most readers to understand
1778:for 6 or 7 extra space-like dimensions all with a
1361:) or else multiply connected (for example, like a
2802:"The Status of Cosmic Topology after Planck Data"
2473:Monthly Notices of the Royal Astronomical Society
1236:and measuring the power spectrum and temperature
3041:
2084:; LachiĂšze-Rey, Marc (1995). "Cosmic Topology".
1280:FriedmannâLemaĂźtreâRobertsonâWalker (FLRW) model
1653:, and can be thought of as a three-dimensional
1601:
926:. Studies show that the observable universe is
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2620:
2076:
2074:
2072:
1649:A positively curved universe is described by
1314:
911:, but in practice, we can only see up to the
782:
2791:: CS1 maint: multiple names: authors list (
2608:
1719:
949:
817:(which itself is constrained by curvature).
1402:
64:Learn how and when to remove these messages
2069:
1622:. The most familiar is the aforementioned
1101:Scientists could experimentally calculate
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2835:
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2003:
1949:
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1841:
1391:such that all points are within distance
1125:), relativistic particles (predominantly
194:Learn how and when to remove this message
176:Learn how and when to remove this message
160:, without removing the technical details.
121:Learn how and when to remove this message
16:Local and global geometry of the universe
2869:
1764:-shaped universe; an alternative to the
1441:
1024:
2135:
2133:
1788: â Historical concept in cosmology
1014:Curved geometries are in the domain of
3042:
2952:What do you mean the universe is flat?
2199:
2050:
1820: â Cartesian product of 3 circles
922:years after the big bang) as anything
2526:Planck Collaboration; Ade, P. A. R.;
2397:
2053:Space and time in the modern universe
1892:
1873:
1786:History of the center of the Universe
1774: â Theory of subatomic structure
1729:(i.e., compact without boundary) and
1369:
837:space is infinite in extent (such as
158:make it understandable to non-experts
2326:
2130:
1307:), it is on average homogeneous and
1111:Wilkinson Microwave Anisotropy Probe
132:
70:
29:
1849:"Will the Universe expand forever?"
1735:FriedmannâLemaĂźtreâRobertsonâWalker
1452:cosmic web of large-scale structure
1305:large-scale structure of the cosmos
25:Journey to the Edge of the Universe
13:
2926:(Pi and the size of the Universe)"
517:2dF Galaxy Redshift Survey ("2dF")
14:
3081:
2916:
2679:
2615:"Is the universe a dodecahedron?"
1818:Three-torus model of the universe
1772:Extra dimensions in string theory
1395:of each other. The smallest such
732:Timeline of cosmological theories
497:Cosmic Background Explorer (COBE)
45:This article has multiple issues.
3027:
3015:
3003:
2991:
2979:
2967:
2504:10.1111/j.1365-2966.2009.14938.x
1695:Universe with negative curvature
1645:Universe with positive curvature
869:Shape of the observable universe
844:Current observational evidence (
756:
745:
744:
137:
75:
34:
2902:10.1590/S0103-97332002000500012
2596:from the original on 2021-12-15
2576:
2519:
2460:
512:Sloan Digital Sky Survey (SDSS)
365:Future of an expanding universe
53:or discuss these issues on the
3065:Unsolved problems in astronomy
3060:Physical cosmological concepts
2430:10.1088/0264-9381/29/16/165006
2055:. cambridge university press.
2044:
1982:
1925:
1901:
1886:
1874:Biron, Lauren (7 April 2015).
1097:, there is negative curvature.
1090:, there is positive curvature.
865:by astronomical observations.
727:History of the Big Bang theory
523:Wilkinson Microwave Anisotropy
1:
2694:Classical and Quantum Gravity
2630:Classical and Quantum Gravity
2407:Classical and Quantum Gravity
1913:hyperphysics.phy-astr.gsu.edu
1834:
1632:ultimate fate of the universe
1602:Universe with zero curvature
881:Distance measures (cosmology)
719:Discovery of cosmic microwave
370:Ultimate fate of the universe
2872:Brazilian Journal of Physics
2771:10.1016/0370-1573(94)00085-H
2532:Astronomy & Astrophysics
2336:Astronomy & Astrophysics
2265:Astronomy & Astrophysics
2116:10.1016/0370-1573(94)00085-h
1938:Astronomy & Astrophysics
1457:
1319:Global structure covers the
7:
2661:10.1088/0264-9381/21/21/010
2562:10.1051/0004-6361/201833910
2367:10.1051/0004-6361/200911881
1968:10.1051/0004-6361/201321591
1798:List of cosmology paradoxes
1740:
1673:Poincaré dodecahedral space
1663:Poincaré dodecahedral space
913:cosmic microwave background
862:curvature density parameter
487:Black Hole Initiative (BHI)
101:the claims made and adding
23:. For the documentary, see
21:Edge of the Universe (song)
10:
3086:
2724:10.1088/0264-9381/15/9/015
2296:10.1051/0004-6361:20064979
2241:10.1051/0004-6361:20078777
2211:Astronomy and Astrophysics
1909:"Density Parameter, Omega"
1315:Global universal structure
1071:, represented with Omega (
953:
878:
872:
250:Chronology of the universe
18:
2051:Davies, P. C. W. (1977).
1720:Curvature: open or closed
1683:, which is very close to
1637:A flat universe can have
1295:the universe is "weakly"
950:Curvature of the universe
343:Expansion of the universe
2686:Geometry of the Universe
2617:, article at PhysicsWeb.
1681:binary icosahedral group
1483:local to global theorems
1403:With or without boundary
1347:whether the universe is
507:Planck space observatory
293:Gravitational wave (GWB)
2837:10.3390/universe2010001
2554:2020A&A...641A...6P
2359:2009A&A...502...27R
2288:2007A&A...463..861R
2233:2008A&A...482..747L
1960:2014A&A...571A..16P
1706:Mostow rigidity theorem
1679:of the 3-sphere by the
1432:differentiable manifold
1083:, the universe is flat.
934:on the largest scales.
360:Inhomogeneous cosmology
2800:Luminet, J.P. (2016).
1876:"Our universe is Flat"
1702:hyperbolic 3-manifolds
1556:, negative curvature:
1113:(WMAP) as well as the
1061:
1016:non-Euclidean geometry
956:Curvature § Space
3050:Differential geometry
1792:Holographic principle
1503:Final results of the
1442:Observational methods
1267:, we can approximate
1139:cosmological constant
1028:
954:Further information:
924:beyond that is opaque
451:Large-scale structure
429:Shape of the universe
2141:Luminet, Jean-Pierre
2082:Luminet, Jean-Pierre
1880:symmetrymagazine.org
1827:Zero-energy universe
1685:icosahedral symmetry
1665:), all of which are
1659:spherical 3-manifold
1620:Bieberbach manifolds
1351:or finite in extent,
1242:BOOMERanG experiment
763:Astronomy portal
721:background radiation
698:List of cosmologists
2894:2002BrJPh..32..891F
2828:2016Univ....2....1L
2763:1995PhR...254..135L
2716:1998CQGra..15.2689L
2653:2004CQGra..21.4901A
2495:2009MNRAS.397..431V
2177:10.1038/nature01944
2169:2003Natur.425..593L
2108:1995PhR...254..135L
2014:2000Natur.404..955D
1689:Jean-Pierre Luminet
1491:Thurston geometries
1487:Riemannian geometry
1334:topological defects
1284:Friedmann equations
1265:spacetime intervals
1046:hyperbolic universe
978:Pythagorean theorem
875:Observable universe
805:, the shape of the
463:Structure formation
355:Friedmann equations
245:Age of the universe
209:Part of a series on
3055:General relativity
2860:possible universes
2858:Classification of
1766:Hot Big Bang Model
1754:Ekpyrotic universe
1577:, zero curvature:
1370:Infinite or finite
1338:hyperbolic 3-space
1273:Euclidean geometry
1227:10 kg⋅m
1065:General relativity
1062:
1038:spherical universe
1031:density parameter
827:multiply connected
819:General relativity
502:Dark Energy Survey
446:Large quasar group
215:Physical cosmology
86:possibly contains
2637:(21): 4901â4926.
2153:(6958): 593â595.
2062:978-0-521-29151-4
1855:. 24 January 2014
1804:Theorema Egregium
1669:of the 3-sphere.
1651:elliptic geometry
1639:zero total energy
1330:geodesic manifold
1115:Planck spacecraft
1069:density parameter
799:
798:
470:
469:
312:
311:
204:
203:
196:
186:
185:
178:
131:
130:
123:
88:original research
68:
3077:
3032:
3031:
3020:
3019:
3018:
3008:
3007:
3006:
2996:
2995:
2994:
2984:
2983:
2972:
2971:
2970:
2963:
2948:
2946:
2945:
2936:. Archived from
2922:
2913:
2887:
2849:
2839:
2821:
2796:
2790:
2782:
2756:
2735:
2709:
2700:(9): 2689â2697.
2688:at icosmos.co.uk
2673:
2672:
2646:
2644:astro-ph/0403597
2624:
2618:
2612:
2606:
2605:
2603:
2601:
2580:
2574:
2573:
2547:
2523:
2517:
2516:
2506:
2488:
2464:
2458:
2457:
2423:
2401:
2395:
2394:
2352:
2330:
2324:
2323:
2281:
2279:astro-ph/0602159
2259:
2253:
2252:
2226:
2206:
2197:
2196:
2162:
2160:astro-ph/0310253
2137:
2128:
2127:
2101:
2078:
2067:
2066:
2048:
2042:
2041:
2022:10.1038/35010035
2007:
2005:astro-ph/0004404
1986:
1980:
1979:
1953:
1929:
1923:
1922:
1920:
1919:
1905:
1899:
1898:
1890:
1884:
1883:
1882:. FermiLab/SLAC.
1871:
1865:
1864:
1862:
1860:
1845:
1823:
1777:
1758:five-dimensional
1657:, or some other
1624:3-torus universe
1597:
1593:
1583:
1576:
1572:
1562:
1555:
1551:
1541:
1534:
1532:
1526:
1468:simply connected
1398:
1394:
1390:
1386:
1382:
1271:by the familiar
1258:
1257:
1255:
1228:
1226:
1210:
1208:
1184:
1182:
1170:
1168:
1156:
1154:
1104:
1096:
1089:
1082:
1074:
1059:
1051:
1043:
1034:
1009:
1003:hyperbolic space
997:
985:
960:Flatness problem
921:
920:
835:simply connected
791:
784:
777:
761:
760:
759:
748:
747:
441:Galaxy formation
401:Lambda-CDM model
390:
389:
382:Components
264:
263:
225:
206:
205:
199:
192:
181:
174:
170:
167:
161:
141:
140:
133:
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103:inline citations
79:
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30:
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2784:
2783:
2741:Physics Reports
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2597:
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2138:
2131:
2086:Physics Reports
2079:
2070:
2063:
2049:
2045:
1998:(6781): 955â9.
1987:
1983:
1932:Ade, P. A. R.;
1930:
1926:
1917:
1915:
1907:
1906:
1902:
1891:
1887:
1872:
1868:
1858:
1856:
1847:
1846:
1842:
1837:
1832:
1821:
1775:
1748:de Sitter space
1743:
1727:closed manifold
1722:
1697:
1647:
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1444:
1436:closed manifold
1405:
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1119:baryonic matter
1102:
1094:
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1080:
1072:
1057:
1049:
1041:
1032:
1005:
993:
981:
970:isotropic space
962:
952:
918:
916:
915:(CMB) (roughly
883:
877:
871:
858:margin of error
839:Euclidean space
795:
757:
755:
737:
736:
723:
720:
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711:Subject history
703:
702:
694:
539:
531:
530:
527:
524:
482:
472:
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434:Galaxy filament
387:
375:
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321:Expansion
314:
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298:Microwave (CMB)
277:Nucleosynthesis
261:
200:
189:
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154:help improve it
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2955:
2949:
2923:
2917:Grime, James.
2914:
2878:(4): 891â894.
2867:
2856:
2850:
2797:
2747:(3): 135â214.
2736:
2689:
2681:
2680:External links
2678:
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2607:
2575:
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2479:(1): 431â444.
2459:
2414:(16): 165006.
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2129:
2092:(3): 135â214.
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1288:fluid dynamics
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2999:
2989:
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2965:
2964:
2961:
2953:
2950:
2940:on 2015-04-30
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2885:gr-qc/0112078
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2754:gr-qc/9605010
2750:
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2707:gr-qc/9803026
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2100:
2099:gr-qc/9605010
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2019:
2015:
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1897:. p. 31.
1896:
1895:New Scientist
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1732:
1731:open manifold
1728:
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1711:
1707:
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1661:(such as the
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1298:
1297:inhomogeneous
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1078:
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1054:flat universe
1047:
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1835:References
1476:flat torus
1332:, free of
1238:anisotropy
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879:See also:
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538:Scientists
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